The first exploit for the new firmware 5.5.2 of the Wii U is currently under development, however the exploit still has a very low success rate.
Prepare the needed files
- prepare your FAT32 SD card with Homebrew launcher, and preferably Haxchi installer to get a persistent and more stable entry point for homebrew. Extract the homebrew launcher 1.4 on your SD card.
If you plan to install Haxchi, be sure you already have a compatible NDS game installed on NAND.
Prepare any other homebrew you want to use, for example Homebrew App Store.
Find a web host or create your own
Visit a website hosting it, like https://fordlae.github.io/ffhax/, http://wiiu.insanenutter.com, http://www.wiiubru.com/x or http://u.drg.li/ or host the sources on your computer.
If it's on your computer, you need python installed, and launch "startServer.bat" on windows, or use any other webserver you want.
Run the browser hack on WiiU
Clear your browser's data, launch the browser again.
Open the server's URL in your browser, or your computer's IP if you are hosting it yourself. Select Exploit
If it freezes, shutdown and try this step again. It can be quick if you are lucky, or taking hours of retries...
If it works, use that opportunity to install haxchi, it will be more stable.
Note: As it is still in beta test phase, http://u.drg.li/ is hosting different versions of that exploit. You should prefer it over other currently available web hosts, and select exploits from delta 0 to 4 until one works (2 seems to be the one is working the most).
If your screen goes grey-white but your console freezes, that's the correct delta, so keep trying that exploit number.
Update the hack
It's currently in development for stability, you might already have an outdated version. Check the "commits" number to know if it has been updated since your last check. Maybe the website you are using or your own files hosted on your computer are old. Try another website or update your files.